基于小波尺度函数的WSK-SV算法及其气动性能预测

WSK-SV algorithm based on scaling function of wavelet and its prediction for aerodynamic performance

提出了一种将小波的尺度函数与SV(support vector)算法相结合的WSK-SV(wavelet scalingkernel-support vector)新算法,并将Daubechies小波以及Shannon小波的尺度函数分别构成尺度核函数,而且分别作为SV算法中一个可容许的支持向量核函数使用.该算法充分利用了Daubechies小波函数的紧支集与正交等特点以及小波的MRA(multi-resolution analysis,多分辨分析),并注意了尺度核函数能够满足Mercer条件.该算法除了具有通常SVM(support vector machine)所具有的优点外,还具有很好的收敛性以及泛化能力,能够有效地提高学习与预测效率.典型算例选取了不同的小波尺度函数,数值计算表明:在一维、二维和三维问题中,这些小波的尺度函数均可以用于WSK-SV算法,进而显示了这个新算法的可行性与通用性.

A new wavelet scaling kernel-support vector（WSK-SV） algorithm based on scaling function of wavelet and support vector（SV） algorithm was presented in this paper,which firstly took Daubechies and Shannon wavelet-scaling kernel function for a kind of admissible support vector kernel,respectively.WSK-SV algorithm possesses such properties as compactly supported wavelet bases,orthogonal bases,multiresolution analysis（MRA）,and satisfies Mercer condition for scaling kernel function.This algorithm not only has the advantages of general support vector machine（SVM）,but also has a good convergence and excellent capacity of generalization,which can improve the learning efficiency and predicting ability.Numerical experiments demonstrate that this proposed WSK-SV algorithm is feasible and effective.